
where \(c_i \colon d \times [0, T] \rightarrow \mathbb {R}^+\)  are the \(i\) -th ionic species concentrations, \(z_i \in \mathbb {Z}\)  are corresponding valences, \(D_i > 0\)  are constant diffusivities, \(\Phi \colon d \times [0, T] \rightarrow \mathbb {R}\)  is the nondimensional electrical potential, \(\rho \colon d \times [0, T] \rightarrow \mathbb {R}\)  is the nondimensional charge density, \(u \colon d \times [0, T] \rightarrow d\)  is the fluid velocity field, \(p \colon d \times [0, T] \rightarrow \mathbb {R}\)  is the fluid pressure, and \(\varepsilon > 0\)  is a constant proportional to the square of the Debye length [1]}, [2]}. Here, \(d = 2, 3\)  is the space dimension and \(d\)  is a \(d\) -dimensional torus.
